Atomic Structure, Isotopes and Relative Atomic Mass

Every atom is built from three subatomic particles: protons, neutrons and electrons. Protons and neutrons sit together in the central nucleus; electrons occupy the space around it.

Each particle has a relative electrical charge:

Particle	Relative charge	Where it is
Proton	+1	In the nucleus
Neutron	0	In the nucleus
Electron	−1	Around the nucleus

Because a proton is +1 and an electron is −1, they cancel exactly. In a neutral atom the number of electrons equals the number of protons, so the positive and negative charges balance and the atom has no overall charge.

If the numbers of protons and electrons are not equal, the particle is an ion, not a neutral atom. Losing electrons gives a positive ion; gaining electrons gives a negative ion.

This balance of charge is the reason atoms are neutral, and it is the starting point for working out the make-up of any atom or ion.

Two numbers describe any atom. The atomic number is the number of protons. The mass number is the total number of protons and neutrons.

The atomic number defines the element. All atoms of a given element have the same number of protons, and different elements have different numbers of protons. Change the number of protons and you have a different element entirely.

Atoms are written with the mass number on top and the atomic number on the bottom, before the symbol. For sodium:

${}_{11}^{23}\text{Na}$

From this you can read off everything:

• Atomic number = 11 → 11 protons
• A neutral atom has equal protons and electrons → 11 electrons
• Neutrons = mass number − atomic number = 23 − 11 = 12 neutrons

Worked example — an ion. For ${}_{12}^{24}{\text{Mg}}^{2+}$: protons = 12, neutrons = 24 − 12 = 12. The 2+ charge means the atom has lost 2 electrons, so electrons = 12 − 2 = 10.

Atoms are extraordinarily small. The radius of an atom is about 0.1 nm, which is $1\times 10^{-10}$ m.

The nucleus is far smaller still: its radius is less than 1/10 000 of the radius of the whole atom, roughly $1\times 10^{-14}$ m. Almost all of the atom is empty space, with the electrons occupying the volume around the tiny nucleus.

Feature	Approximate radius
Whole atom	0.1 nm = $1\times 10^{-10}$ m
Nucleus	about $1\times 10^{-14}$ m (< 1/10 000 of the atom)

Yet despite its tiny size, almost all of the mass of the atom is in the nucleus, because protons and neutrons carry the mass while electrons are nearly massless.

To picture the scale: if an atom were the size of a large sports stadium, the nucleus would be about the size of a pea at the centre. Everything else is the space where the electrons are found.

The relative masses of the particles make this clear: a proton and a neutron each have a relative mass of 1, while the electron's relative mass is so small it is treated as very small (effectively negligible).

Isotopes are atoms of the same element with different numbers of neutrons. They have the same number of protons (so the same atomic number) but different mass numbers.

Chlorine, for example, exists as two isotopes:

Isotope	Protons	Neutrons	Mass number
Chlorine-35	17	18	35
Chlorine-37	17	20	37

Both are chlorine because both have 17 protons. They differ only in neutron number, which changes the mass but not the identity of the element.

Isotopes of an element have the same chemical properties, because chemical reactions depend on the electrons, and isotopes have the same number of electrons arranged in the same way. Only physical properties that depend on mass, such as density, differ slightly.

Because most elements are a mixture of isotopes, we use an average mass called the relative atomic mass (Ar). It is an average value that takes account of the abundance of each isotope — a weighted average, not a simple one.

The formula is:

$A_r=\frac{\sum (\text{isotope mass number}\times \text{percentage abundance})}{100}$

Worked example 1 — chlorine. Chlorine is 75% chlorine-35 and 25% chlorine-37.

$A_r=\frac{(35\times 75)+(37\times 25)}{100}=\frac{2625+925}{100}=\frac{3550}{100}=35.5$

The answer, 35.5, is closer to 35 than to 37 because the lighter isotope is more abundant. That matches the value on the periodic table.

Worked example 2 — boron. Boron is 20% boron-10 and 80% boron-11.

$A_r=\frac{(10\times 20)+(11\times 80)}{100}=\frac{200+880}{100}=\frac{1080}{100}=10.8$

The result, 10.8, lies close to 11 because boron-11 is the more abundant isotope.

1. Confusing atomic number and mass number

Atomic number is the number of protons and defines the element; mass number is protons plus neutrons. To find neutrons, subtract atomic number from mass number, not the other way round.

2. Forgetting to adjust electrons for an ion

A neutral atom has equal protons and electrons, but an ion does not. A 2+ ion has lost 2 electrons; a 1− ion has gained 1. Adjust the electron count using the charge.

3. Treating relative atomic mass as a simple average

Ar is a weighted average by abundance, so you multiply each isotope mass by its percentage before adding. Simply averaging 35 and 37 to get 36 for chlorine is wrong; the answer is 35.5.

4. Dividing by the wrong number

After summing (mass × percentage) for each isotope, divide by 100 when abundances are percentages (or by the total abundance if fractions are given). Dividing by the number of isotopes instead gives a wrong Ar.

5. Saying isotopes react differently

Isotopes have the same electronic structure, so they behave the same in chemical reactions. Only mass-dependent physical properties differ, so do not claim one isotope is more reactive than another.